The selforganization phenomenon in Rayleigh-Benard convection: a hydrodynamics analysis

TL;DR

This paper reviews the hydrodynamics of Rayleigh-Bénard convection, focusing on pattern formation and flow evolution, supported by theoretical analysis and numerical simulations under the Boussinesq approximation.

Contribution

It provides new numerical findings and a simplified 2D analysis of pattern formation in Rayleigh-Bénard convection, enhancing understanding of flow self-organization.

Findings

Flow evolves towards an optimal form

Pattern formation is theoretically characterized

Numerical simulations support theoretical predictions

Abstract

The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is well studied. Here we review results from the investigation of this system as well as a number of related and novel numerical findings. We present theoretical results for pattern formation in Rayleigh-B\'enard convection with solving NS equation under the Boussinesq approximation . System of equations were reduced to 2-dimension form to simplify the analysis.The evolution of the flow agree with the idea of the flow achieving an optimal form.